The Position Offset allows you to move where along the entire path's length that it positions the raster or text layer. A circular path has a node that acts as both the beginning and end of the path, which means that wherever that node lies is sort of a boundary that an Along Paths won't be able to cross. I realized this a while ago and haven't thought about different solutions yet. For now you'll just have to rotate the paths-layer so that the boundary node is on the opposite side of it from where you want your raster/text to be mapped to.
I think the simplest thing to do is just make it so that the 0.0->1.0 value range goes farther with continuous/looping paths, so that the raster/text can be seamlessly mapped around the entire path. I'll have to take a look and see what needs to be done.